Arch dam



May 19, 1931. L R. JORGENSEN ARCH DAM Filed May 28. 1929 4 Sheets-Sheet1 Q INVENTOR.

TTORNEYS.

May 19, 1931. L. R. JORGENSEN 1,305,986

ARCH DAM Filed May 28, 1929 4 Sheets-Sheet 2 IN V EN TOR.

A TTORNEYS.

cl w LJXU YW May 19, 1931. l... R. JORGENSEN ARCH DAM Filed May 28, 19294 Sheets-Sheet o INVENTOR. 0/ 2 11 fllf IIJI'H 3 BY W W w p A TTORNrfYS.

4 Sheets-Sheet 4 L R. JORGENSEN ARCH DAM Filed May 28, 1929 May 19,1931.

kWQ 5 3 b 3 cm NMH INVENTOR.

TORNEYS.

Patented May 19, 1931 LABS R. JORGENSEN, OF

PATENT OFFICE BERKELEY, CALIFORNIA ARCH DAM Application filed May 28,

and as near to 120 as possible, as has been fully disclosed anddescribed in my former Patent Number 986,718. This is easilyaccomplished in a U-shaped canyon, but it is seldom possible in apronounced V, or invertedA shaped canyon. Even where a considerableoverhang is allowed at the abutments, the subtended angle will be foundto decrease in value towards lower elevations, where the structure isdesigned to fit ordinary canyons. In other words, the arch becomesflatter towards the foundation, and therefore more inefficient.

For the purpose of explaining and describing the dam structure formingthe subject matter of the present application, I refer to the dam asbeing divided horizontally into three zones; a top or upper zone; amiddle zone; and a bottom Zone.

The object of the present invention is to improve the shape of thearches of the several zons so as to increase strength, and at the sametime reduce the amount of material required to a minimum. The invention,more specifically stated consists in shaping the arches in the top zoneat the abutments in such a manner as to obtain the roundest possiblearch with a minimum of overhang. The arch is. in this manner, given anelliptical shape, flatter at the crown than at the abutments. At andtowards the top the arches are to be designed as three centered archesor the like, in a horizontal plane, with the shorter radius curves atthe abutments.

In the so-called middle zone the arch may be designed as an ordinaryarch except that it is made thicker at the abutments than at the crown.In the bottom zone the arch may be designed as an ordinary arch exceptat and towards the foundation, where the arch is made thicker at thecrown than at the abutments to take care of the larger amount of 1929.Serial No. 366,578.

shear ordinarily present in this part of the structure. Should the spanat the bottom be rather long, it is possible to keep a large subtendedangle, thereby enabling a large proportion of the load to be taken byactual arch action. In that case the upstream face is brought upstreamat the abutments by means of a short tangent or reverse curve. This willcause any possible overhang to be filled out, and furthermore enablesthe abutments to take better care of bending stresses.

In order to still further increase the size of the subtended angle, ormaintain it at a larger value towards lower elevations, the top zone ofthe dam is given a slope in a downstream direction in such a manner thatthe central part of the dam at and near the crest overhangs the middlezone on the downstream side. The downstream face of the middle zonewill, in that instance, be madesubstantially vertical, and thedownstream face of the bottom zone will slopein a downstream directiontowards lower elevations in the usual manner.

By constructing arch dams in most V, or inverted A-shaped canyons, asexplained above, the length of the upstream radius at different lowerelevations can be made to decrease towards the bottom at a greater ratethan has been made possible heretofore, assuming. of course, that areasonable amount of overhang will be used at the abutments in bothcases. Since the thickness of the arch is proportional to the upstreamradius, the importance of decreasing the length of the upstream radiusshould at once be apparent.

The dam structure is shown by way of illustration in the accompanyingdrawings, in which:

Fig. 1 is a plan view of the dam,

Fig. 2 is a vertical cross section of the dam taken on line IIII, Fig.1,

Fig. 3 is a plan view of the top zone of the dam,

Fig. 4 is a plan view of the middle zone of the dam,

Fig. 5 is a plan view of the lower zone of the dam as it would appear ina narrow canyon,

Fig. 6 is a plan view of the lower or bottom zone showing a modificationof the up- Inn stream face to avoid the overhang and to increase thethickness of the abutments so as to resist bending where the canyon iswide at the bottom.

For the purpose of description it will here be stated that the dam andthe dam site illustrated are merely imaginary. It will also be statedthat the dam must beconsidered as being'divided horizontally into threesuperposed zones, to wit, a top zone, a middle zone and a bottom zone.The division of the body of the dam into the zones specified is anarbitrary one for the sake of clearness. The imaginary dam illustratedin this instance is one hundred and fifty feet high, and each of thethree zones are shown as fifty feet in height. For an actual dam whichhas to fit a rough canyon no such regularit is possible.

hen the design of such a dam is commenced, the procedure is from thecrest and downward.

The top contours are here indicated at OO, and the top arch is laid outto subtend an angle of say 120. The arch is, however, not carried clearto the abutments with one radius but shorter radii are used at theabutments, which brings the arch further back in a downstream directionat the abutments than otherwise. This is indicated in Fig. 3 by dottedlines aa which represents a continuation of the arch as laid out for thecentral portion.

The arch at contours and is laid out inthe same manner only the arch isbent back at the abutments a less amount towards lower elevations. Atelevation 40 there is nothing gained in bending the arch back for thisimaginary site and, therefore, it is not done at this elevation, but themaximum allowable overhang is maintained if necessary for economys sake.

An overhang of three to four feet at the abutments is generallyconsidered good practice. The arch butting into the abutment atelevation 10 has about that amount of overhang, as indicated at I), butit is plainly seen from Fig. 3 that if the ends of the arch at elevation0 had not been bent in a downstream direction the overhang C would havebeen nearly twice as large.

, The more overhang one is willing to take, the shorter the upstreamradii can be made at lower elevations and, therefore economy, as far asconcrete is concerned, is kept high. More than a certain overhang cannotbe tolerated structurally, but it is seen that by bending the archesback at the abutments near the crest the benefit of nearly double theallowable overhang may be obtained lower down, besides the line ofpressure in such an arch will more nearly coincide with the centerlineof the arch' than it would in a perfectly circular arch.

An actual canyon may be shaped such that this scheme can be used atlower elevations also to diminish the length of the upstream radii atlower elevations. At the same time the bending back of the arch at theabutments has a tendency to relieve the bending stresses in the arch atthe abutments, where they are the highest.

Fig. 3 shows a considerable overhang of the dam near the center abovethe river, as indicated at 13. Another view of this same overhang isshown in Fig. 2. The purpose of this overhang is the same as that ofbendin g back the arch at the abutments, namely, to be able to stillfurther shorten the upstream radii at lower elevations. It is seen, thateach lower arch slice is so to speak pushed upstream in relation to anyother arch above, thus enabling a rounder arch to be inscribed withoutincreasing the amount of overhang at the abutments above that assumed asallowable.

In Fig. 4 the so-called middle zone of the dam is shown. In a narrowcanyon overhang on the upstream face at the abutments would most likelynot be used, whereas, for a dam in a wide canyon it would be used. Thedown stream face of the dam may either be struck from a center locatedupstream of the center for the corresponding upstream face in which casethe thickness of the arch would be gradually increased from crown toabutment, or the same center for up and downstream faces may be usedwith some additional material placed at and nearthe abutments toincrease the thickness where it is most necessary.

In Fig. 5 the lower zone is shown. This represents a fairly narrowcanyon in which overhang on the upstream side at the abutments canseldom be used to advantage in a commercial design: The arch is thick.with relation to its length and acts more like a beam. The downstreamface at and below contour 110 is struck from one center as indi-" catedat Fig. 5. This makes the arch below' contour 110 thicker at and nearits central portion. This extra material is active in resisting thehorizontal bending moment in the arch, the possible Vertical bendingmoment in the cantilever besidesthe cantilever shear.

In Fig. 6 the same lower zone of the dam is shown, but in a wide canyon.What would otherwise be a considerable overhang is filled out withmaterial (concrete) to a tangent or reverse curve, such as shown at f.The material added increases the thickness of the abutments. The archaction is more effective in the wider canyon than in the narrow oneshown in Fig. 5, and therefore it is logical to increase the thicknessat the abutments either on the upstream side or downstream side, or onboth sides.

At the very bottom the center for the downstream face may be located ina downstream direction with relation to the center for the upstreamface, the same as shown in Fig. 5, this is a matter of design.

Having thus described my invention, what I claim and desire to secure byLetters Patent 1s:

1. In a constant angle arch dam which is divided horizontally into abottom, a middle and a top zone, and where said zones are superposed thetop zone having the ends of the arches of sharper curvature towards theabutments than the central part of the arches, the central part of saidarches projecting partly outside the middle zone on the downstream side,the amount of projection being maximum at the crown of the arch anddiminishing to zero towards the haunches and towards lower elevations.

2. In a constant angle arch dam which is divided horizontally into abottom, a middle and a top zone, where said zones are superposed the topzone having the ends of the arches of sharper curvature towards theabutments than the central part of the arches, the central part of saidarches projecting partly outside the middle zone on the downstream side,the amount of projection being maximum at the crown of the arch anddiminishing to zero towards the haunches and towards lower elevations,the middle zone presenting a substantially vertical face on thedownstream side in the center. and having faces consisting ofsubstantially circular arches which are substantially concentric anduniform in thickness from the center to the abutments, the lower zonehaving substantially circular arches with additional material placed onthe upstream side at and towards the abutments.

3. In a constant angle arch dam which is divided horizontally into abottom, a middle and a top zone, where said zones are super posed thetop zone having the ends of the arches of sharper curvature towards theabutments than the central part of the arches, the top zone of the damprojecting partly outside the middle zone on the downstream side, the.amount of rojection being a maximum at the crown oi the arch anddiminishing to zero and towards lower elevations, the mlddle zone beingsubstantially vertical on the downstream side in the center and havingfaces consisting of substantially circular arches which aresubstantially concentric and uniform in thickness from the center to theabutments.

4. In a constant angle arch dam which is divided horizontally into abottom, a middle and a top zone, where said zones are superposed the topzone having the ends of the arches of sharper curvature towards theabutments than the central part of the arches, the top zone of the damprojecting partly outside the middlezone on the downstream side, theamount of rojection being a maximum at the crown o the arch and diminishing to zero and towards lower elevations, the middle zone beingsubstantially vertical on the downstream side in the center, havingfaces consisting of substantially circular arches which aresubstantially concentric and uniform in thickness from the center to theabutments, and the bottom zone having substantially circular arches withadditional material placed on the upstream side at and towards theabutments.

5. An arch dam having the central part of the arch leaning in adownstream direction, and the end portions of the arch leaning in anupstream direction.

6. A constant angle arch dam having the central part of the arch leaningin a downstream direction, and the end portions of the arch leaning inan upstream direction, the up and downstream faces forming warpedsurfaces both in vertical and horizontal planes.

7. In a constant angle arch dam which is divided horizontally into abottom, a middle and a top zone and where said zones are superposed, thecenter part of the upper zone of the arch having an overhang leaning ina downstream direction and end portions of the upper zone of the archhaving an overhang leaning in an upstream direction.

LARS R. JORGENSEN.

